NUPACK: Model

Secondary Structure Model

The secondary structure of multiple interacting strands is defined by a list of base pairs (Dirks et al., 2007). A polymer graph for a secondary structure can be constructed by ordering the strands around a circle, drawing the backbones in succession from 5’ to 3’ around the circumference with a nick between each strand, and drawing straight lines connecting paired bases. A secondary structure is pseudoknotted if every strand ordering corresponds to a polymer graph with crossing lines. A secondary structure is connected if no subset of the strands is free of the others. Algorithms are formulated in terms of ordered complexes (Zadeh et al.; Dirks et al., 2007), each corresponding to the structural ensemble of all connected polymer graphs with no crossing lines for a particular ordering of a set of strands. The free energy of an unpseudoknotted secondary structure is calculated using nearest-neighbor empirical parameters for RNA in 1M Na⁺ (Serra and Turner, 1995; Mathews et al., 1999) or DNA in user-specified Na⁺ and Mg⁺⁺ concentrations (SantaLucia, 1998; SantaLucia and Hicks, 2004; Koehler and Peyret, 2005); additional parameters are employed for the analysis of RNA pseudoknots (Dirks and Pierce, 2003).

References

Dirks, R.M., J.S. Bois, J.M. Schaeffer, E. Winfree and N.A. Pierce (2007). Thermodynamic analysis of interacting nucleic acid strands. SIAM Rev 49: 65-88.
Dirks, R.M. and N.A. Pierce (2003). A partition function algorithm for nucleic acid secondary structure including pseudoknots. J Comput Chem 24: 1664-1677.
Koehler, R.T. and N. Peyret (2005). Thermodynamic properties of DNA sequences: characteristic values for the human genome. Bioinformatics 21: 3333-3339.
Mathews, D.H., J. Sabina, M. Zuker and D.H. Turner (1999). Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J Mol Biol 288: 911-940.
SantaLucia, J. and D. Hicks (2004). The thermodynamics of DNA structural motifs. Annu Rev Bioph Biom 33: 415-440.
SantaLucia, J. (1998). A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proc Natl Acad Sci USA 95: 1460-1465.
Serra, M.J. and D.H. Turner (1995). Predicting thermodynamic properties of RNA. Methods Enzymol 259: 242-261.
Zadeh, J.N., B.R. Wolfe and N.A. Pierce (Submitted). Nucleic acid sequence design via efficient ensemble optimization.